The Cosmic Ray Muon Detector · AI Generator #GEN-46D8293F

Physics · modern-physics

Problem

A research team builds a cosmic ray detector consisting of two parallel scintillator plates separated by a distance

d = 2.0\;\text{m}

. The detector is designed to measure muons created when cosmic rays interact with the atmosphere at an altitude of

h = 15\;\text{km}

above the detector. Muons have a rest mass

m_0 = 106\;\text{MeV}/c^2

and a proper lifetime

\tau_0 = 2.2 \times 10^{-6}\;\text{s}

. For the detector to register a muon, the muon must pass through both plates while still being alive. The team observes that exactly

37\%

of the muons that enter the top plate successfully pass through both plates and trigger the detector. All muons travel vertically downward at the same speed. (a) What is the speed of the muons as a fraction of the speed of light? (b) What is the total kinetic energy of each muon?

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